A247858 Decimal expansion of the value of the continued fraction [0; 2, 5, 17, 17, 37, 41, 97, 97, ...], generated with primes of the form a^2 + b^4.

4, 5, 5, 0, 2, 4, 8, 1, 6, 4, 9, 0, 1, 7, 0, 0, 2, 2, 3, 6, 9, 0, 5, 2, 8, 0, 8, 2, 7, 9, 7, 4, 4, 8, 2, 4, 1, 0, 5, 7, 5, 5, 5, 4, 8, 9, 0, 5, 0, 7, 6, 4, 4, 0, 5, 6, 8, 5, 4, 1, 8, 5, 9, 1, 5, 0, 8, 4, 6, 0, 8, 5, 0, 1, 0, 7, 1, 8, 6, 3, 1, 4, 3, 6, 3, 1, 0, 6, 6, 7, 6, 9, 7, 5, 4, 6, 0, 4, 5, 1, 9, 9, 2

Offset

0,1

Links

Table of n, a(n) for n=0..102.

John Friedlander and Henryk Iwaniec, Using a parity-sensitive sieve to count prime values of a polynomial, PNAS February 18, 1997 94 (4) 1054-1058.

Wikipedia, Friedlander-Iwaniec theorem

Marek Wolf, Continued fractions constructed from prime numbers, arXiv:1003.4015 [math.NT], 2010, pp. 8-9.

Example

1/(2 + 1/(5 + 1/(17 + 1/(17 + 1/(37 + 1/(41 + 1/(97 + 1/(97 + ...))))))))
0.45502481649017002236905280827974482410575554890507644...

Mathematica

max = 1000; r = Reap[Do[n = a^2 + b^4; If[n <= max && PrimeQ[n], Sow[n]], {a, Sqrt[max]}, {b, max^(1/4)}]][[2, 1]]; u = Union[r, SameTest -> (False&)] ; RealDigits[FromContinuedFraction[Join[{0}, u]], 10, 103] // First

Crossrefs

Cf. A028916, A243340, A247857.

Sequence in context: A279270 A075464 A332709 * A247860 A196756 A103561

Adjacent sequences: A247855 A247856 A247857 * A247859 A247860 A247861

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 25 2014

Status

approved